from os import path
from math import isfinite
import numpy as np
from gudhi.reader_utils import read_persistence_intervals_in_dimension
from gudhi.reader_utils import read_persistence_intervals_grouped_by_dimension
""" This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
Author(s): Vincent Rouvreau, Bertrand Michel
Copyright (C) 2016 Inria
Modification(s):
- YYYY/MM Author: Description of the modification
"""
__author__ = "Vincent Rouvreau, Bertrand Michel"
__copyright__ = "Copyright (C) 2016 Inria"
__license__ = "MIT"
def __min_birth_max_death(persistence, band=0.0):
"""This function returns (min_birth, max_death) from the persistence.
:param persistence: The persistence to plot.
:type persistence: list of tuples(dimension, tuple(birth, death)).
:param band: band
:type band: float.
:returns: (float, float) -- (min_birth, max_death).
"""
# Look for minimum birth date and maximum death date for plot optimisation
max_death = 0
min_birth = persistence[0][1][0]
for interval in reversed(persistence):
if float(interval[1][1]) != float("inf"):
if float(interval[1][1]) > max_death:
max_death = float(interval[1][1])
if float(interval[1][0]) > max_death:
max_death = float(interval[1][0])
if float(interval[1][0]) < min_birth:
min_birth = float(interval[1][0])
if band > 0.0:
max_death += band
return (min_birth, max_death)
"""
Only 13 colors for the palette
"""
palette = [
"#ff0000",
"#00ff00",
"#0000ff",
"#00ffff",
"#ff00ff",
"#ffff00",
"#000000",
"#880000",
"#008800",
"#000088",
"#888800",
"#880088",
"#008888",
]
[docs]def plot_persistence_barcode(
persistence=[],
persistence_file="",
alpha=0.6,
max_intervals=1000,
max_barcodes=1000,
inf_delta=0.1,
legend=False,
):
"""This function plots the persistence bar code from persistence values list
or from a :doc:`persistence file <fileformats>`.
:param persistence: Persistence intervals values list grouped by dimension.
:type persistence: list of tuples(dimension, tuple(birth, death)).
:param persistence_file: A :doc:`persistence file <fileformats>` style name
(reset persistence if both are set).
:type persistence_file: string
:param alpha: barcode transparency value (0.0 transparent through 1.0
opaque - default is 0.6).
:type alpha: float.
:param max_intervals: maximal number of intervals to display.
Selected intervals are those with the longest life time. Set it
to 0 to see all. Default value is 1000.
:type max_intervals: int.
:param inf_delta: Infinity is placed at :code:`((max_death - min_birth) x
inf_delta)` above :code:`max_death` value. A reasonable value is
between 0.05 and 0.5 - default is 0.1.
:type inf_delta: float.
:param legend: Display the dimension color legend (default is False).
:type legend: boolean.
:returns: A matplotlib object containing horizontal bar plot of persistence
(launch `show()` method on it to display it).
"""
try:
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
if persistence_file is not "":
if path.isfile(persistence_file):
# Reset persistence
persistence = []
diag = read_persistence_intervals_grouped_by_dimension(
persistence_file=persistence_file
)
for key in diag.keys():
for persistence_interval in diag[key]:
persistence.append((key, persistence_interval))
else:
print("file " + persistence_file + " not found.")
return None
if max_barcodes is not 1000:
print("Deprecated parameter. It has been replaced by max_intervals")
max_intervals = max_barcodes
if max_intervals > 0 and max_intervals < len(persistence):
# Sort by life time, then takes only the max_intervals elements
persistence = sorted(
persistence,
key=lambda life_time: life_time[1][1] - life_time[1][0],
reverse=True,
)[:max_intervals]
persistence = sorted(persistence, key=lambda birth: birth[1][0])
(min_birth, max_death) = __min_birth_max_death(persistence)
ind = 0
delta = (max_death - min_birth) * inf_delta
# Replace infinity values with max_death + delta for bar code to be more
# readable
infinity = max_death + delta
axis_start = min_birth - delta
# Draw horizontal bars in loop
for interval in reversed(persistence):
if float(interval[1][1]) != float("inf"):
# Finite death case
plt.barh(
ind,
(interval[1][1] - interval[1][0]),
height=0.8,
left=interval[1][0],
alpha=alpha,
color=palette[interval[0]],
linewidth=0,
)
else:
# Infinite death case for diagram to be nicer
plt.barh(
ind,
(infinity - interval[1][0]),
height=0.8,
left=interval[1][0],
alpha=alpha,
color=palette[interval[0]],
linewidth=0,
)
ind = ind + 1
if legend:
dimensions = list(set(item[0] for item in persistence))
plt.legend(
handles=[
mpatches.Patch(color=palette[dim], label=str(dim))
for dim in dimensions
],
loc="lower right",
)
plt.title("Persistence barcode")
# Ends plot on infinity value and starts a little bit before min_birth
plt.axis([axis_start, infinity, 0, ind])
return plt
except ImportError:
print("This function is not available, you may be missing matplotlib.")
[docs]def plot_persistence_diagram(
persistence=[],
persistence_file="",
alpha=0.6,
band=0.0,
max_intervals=1000,
max_plots=1000,
inf_delta=0.1,
legend=False,
):
"""This function plots the persistence diagram from persistence values
list or from a :doc:`persistence file <fileformats>`.
:param persistence: Persistence intervals values list grouped by dimension.
:type persistence: list of tuples(dimension, tuple(birth, death)).
:param persistence_file: A :doc:`persistence file <fileformats>` style name
(reset persistence if both are set).
:type persistence_file: string
:param alpha: plot transparency value (0.0 transparent through 1.0
opaque - default is 0.6).
:type alpha: float.
:param band: band (not displayed if :math:`\leq` 0. - default is 0.)
:type band: float.
:param max_intervals: maximal number of intervals to display.
Selected intervals are those with the longest life time. Set it
to 0 to see all. Default value is 1000.
:type max_intervals: int.
:param inf_delta: Infinity is placed at :code:`((max_death - min_birth) x
inf_delta)` above :code:`max_death` value. A reasonable value is
between 0.05 and 0.5 - default is 0.1.
:type inf_delta: float.
:param legend: Display the dimension color legend (default is False).
:type legend: boolean.
:returns: A matplotlib object containing diagram plot of persistence
(launch `show()` method on it to display it).
"""
try:
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
if persistence_file is not "":
if path.isfile(persistence_file):
# Reset persistence
persistence = []
diag = read_persistence_intervals_grouped_by_dimension(
persistence_file=persistence_file
)
for key in diag.keys():
for persistence_interval in diag[key]:
persistence.append((key, persistence_interval))
else:
print("file " + persistence_file + " not found.")
return None
if max_plots is not 1000:
print("Deprecated parameter. It has been replaced by max_intervals")
max_intervals = max_plots
if max_intervals > 0 and max_intervals < len(persistence):
# Sort by life time, then takes only the max_intervals elements
persistence = sorted(
persistence,
key=lambda life_time: life_time[1][1] - life_time[1][0],
reverse=True,
)[:max_intervals]
(min_birth, max_death) = __min_birth_max_death(persistence, band)
delta = (max_death - min_birth) * inf_delta
# Replace infinity values with max_death + delta for diagram to be more
# readable
infinity = max_death + delta
axis_start = min_birth - delta
# line display of equation : birth = death
x = np.linspace(axis_start, infinity, 1000)
# infinity line and text
plt.plot(x, x, color="k", linewidth=1.0)
plt.plot(x, [infinity] * len(x), linewidth=1.0, color="k", alpha=alpha)
plt.text(axis_start, infinity, r"$\infty$", color="k", alpha=alpha)
# bootstrap band
if band > 0.0:
plt.fill_between(x, x, x + band, alpha=alpha, facecolor="red")
# Draw points in loop
for interval in reversed(persistence):
if float(interval[1][1]) != float("inf"):
# Finite death case
plt.scatter(
interval[1][0],
interval[1][1],
alpha=alpha,
color=palette[interval[0]],
)
else:
# Infinite death case for diagram to be nicer
plt.scatter(
interval[1][0], infinity, alpha=alpha, color=palette[interval[0]]
)
if legend:
dimensions = list(set(item[0] for item in persistence))
plt.legend(
handles=[
mpatches.Patch(color=palette[dim], label=str(dim))
for dim in dimensions
]
)
plt.title("Persistence diagram")
plt.xlabel("Birth")
plt.ylabel("Death")
# Ends plot on infinity value and starts a little bit before min_birth
plt.axis([axis_start, infinity, axis_start, infinity + delta])
return plt
except ImportError:
print("This function is not available, you may be missing matplotlib.")
[docs]def plot_persistence_density(
persistence=[],
persistence_file="",
nbins=300,
bw_method=None,
max_intervals=1000,
dimension=None,
cmap=None,
legend=False,
):
"""This function plots the persistence density from persistence
values list or from a :doc:`persistence file <fileformats>`. Be
aware that this function does not distinguish the dimension, it is
up to you to select the required one. This function also does not handle
degenerate data set (scipy correlation matrix inversion can fail).
:param persistence: Persistence intervals values list grouped by dimension.
:type persistence: list of tuples(dimension, tuple(birth, death)).
:param persistence_file: A :doc:`persistence file <fileformats>`
style name (reset persistence if both are set).
:type persistence_file: string
:param nbins: Evaluate a gaussian kde on a regular grid of nbins x
nbins over data extents (default is 300)
:type nbins: int.
:param bw_method: The method used to calculate the estimator
bandwidth. This can be 'scott', 'silverman', a scalar constant
or a callable. If a scalar, this will be used directly as
kde.factor. If a callable, it should take a gaussian_kde
instance as only parameter and return a scalar. If None
(default), 'scott' is used. See
`scipy.stats.gaussian_kde documentation
<http://scipy.github.io/devdocs/generated/scipy.stats.gaussian_kde.html>`_
for more details.
:type bw_method: str, scalar or callable, optional.
:param max_intervals: maximal number of points used in the density
estimation.
Selected intervals are those with the longest life time. Set it
to 0 to see all. Default value is 1000.
:type max_intervals: int.
:param dimension: the dimension to be selected in the intervals
(default is None to mix all dimensions).
:type dimension: int.
:param cmap: A matplotlib colormap (default is
matplotlib.pyplot.cm.hot_r).
:type cmap: cf. matplotlib colormap.
:param legend: Display the color bar values (default is False).
:type legend: boolean.
:returns: A matplotlib object containing diagram plot of persistence
(launch `show()` method on it to display it).
"""
try:
import matplotlib.pyplot as plt
from scipy.stats import kde
if persistence_file is not "":
if dimension is None:
# All dimension case
dimension = -1
if path.isfile(persistence_file):
persistence_dim = read_persistence_intervals_in_dimension(
persistence_file=persistence_file, only_this_dim=dimension
)
print(persistence_dim)
else:
print("file " + persistence_file + " not found.")
return None
if len(persistence) > 0:
persistence_dim = np.array(
[
(dim_interval[1][0], dim_interval[1][1])
for dim_interval in persistence
if (dim_interval[0] == dimension) or (dimension is None)
]
)
persistence_dim = persistence_dim[np.isfinite(persistence_dim[:, 1])]
if max_intervals > 0 and max_intervals < len(persistence_dim):
# Sort by life time, then takes only the max_intervals elements
persistence_dim = np.array(
sorted(
persistence_dim,
key=lambda life_time: life_time[1] - life_time[0],
reverse=True,
)[:max_intervals]
)
# Set as numpy array birth and death (remove undefined values - inf and NaN)
birth = persistence_dim[:, 0]
death = persistence_dim[:, 1]
# line display of equation : birth = death
x = np.linspace(death.min(), birth.max(), 1000)
plt.plot(x, x, color="k", linewidth=1.0)
# Evaluate a gaussian kde on a regular grid of nbins x nbins over data extents
k = kde.gaussian_kde([birth, death], bw_method=bw_method)
xi, yi = np.mgrid[
birth.min() : birth.max() : nbins * 1j,
death.min() : death.max() : nbins * 1j,
]
zi = k(np.vstack([xi.flatten(), yi.flatten()]))
# default cmap value cannot be done at argument definition level as matplotlib is not yet defined.
if cmap is None:
cmap = plt.cm.hot_r
# Make the plot
plt.pcolormesh(xi, yi, zi.reshape(xi.shape), cmap=cmap)
if legend:
plt.colorbar()
plt.title("Persistence density")
plt.xlabel("Birth")
plt.ylabel("Death")
return plt
except ImportError:
print(
"This function is not available, you may be missing matplotlib and/or scipy."
)